Wave filter



Aug.21,192s.. A 1,681,554

|-:.L.NQRTON WAVE FILTER Filed Nov. 24, 1924 2 Sheets-Sheet 1` E. L.NORTON WAVE FILTER Aug. 2i, 192s. 1,681,554

Filed NQv. 24, 1924 2 Sheets-Sheet 2 fig] Cae 54 51.9 /fl/g M22 527' pyAny.

Patented Aug. 2l, 192,8.

UNITED A.STATES EDWARD T.. Nontron, on NEW Yonx, N. Y., AssTeNoR froWESTERN ELECTRIC coli:-

PATENT oFFlcE.

EANY, INCORPORATEDVOF NEW YORK, N. Y., A CORPORATION 0F NEW YORK.

WAVE FILTER.

rApplication led November 24, 1924. Serial No. 751,748.

This invention relates to selective wave transmission systems, and moreparticularly to broad band Wave filters.

An obj ect Vof the invention is to combine in a. single device thefunctions of frequencyselection and of Wave motion transformation.

Another object is to increase the transfer of energy in selectivewavesystems having terminalfimpedances of unequal magnitudes.

Another object is to provide a wave filter, either electrical ormechanical, adapted to operate With maximum efficiency between unequalimpedances.

A special objectis to increase the efficiency of rthe translation ofelectric wave energy into the energy of sound waves.

Other objects of the invention will appear from the description whichfollows of the principles and operation of the invention.

The term broad band Wave filter refers to the general class of devicedescribed in U. S. patent to Campbell, 1.227,113, May 27,

1917, and by G. A. Campbell, Physical theory l of the electric wavefilter, Bell System Tech- 1 thc analogous electrical system.

nical Journal, Vol. I-No. 2, November 1922, and again by 0. J. Zobel,Theory anddesign of uniform and composite electric wave filters. BellSystem Techanical Journal, Vol.

H-No- 1, January 1923. In these refer-` ences, the physical theory andthe principles of design are devcoped with particular reference toelectrical systems, but it is recognized that the same principles areapplicable to the discrimination between wave motions of any typeregardless of the medium in which the Waves are transmitted.

One particular embodiment of the invention hereinafter described is in aloud speaking telephone receiver. the electrical, mechanical andacoustical elements of which are arranged to constitute a single broadband filter through which energy is propagated successively by electricwaves, mechanical vibrations. and sound waves.

To elucidate more fully the principles and scope, of the invention.other devices in the form of mechanical wave filters are described,these being particularly chosen to demonstrate the. correspondencebetween the elements of a mechanical system and those of The theory anexample of the latter application.,

sion of maximum energy from a given source is the principal object ofthe design, and t0 attain this it is a Well known proposition that thelmpedances at the junction points of successive sections must beproperly matched-t0' avoid reflection losses. If these impedances arenot naturally equal, the common practice is to insert transformers atthe junction points, the transformation ratios of which compensate theinequality of the impedances. Practical difiiculties, however, make itimpossible to construct transformers that do not dissipate some of theenergy of the waves transmitted through them. They are also limited withrespect to the range of frequencies freely transmitted, low frequencyWaves being attenuated by the 10W impedances of the windings and highfrequency waves being absorbed in the electrostatic capacities of thewindings.

In selective transmission systems, the range of frequencies is purposelylimited by the insertion of band filters.v Also, in certain types ofsystem, which necessarily include chains of functional elements havingreactances of different kinds, it is advantageous to proportion theelements so that they combine to operate as a Wave filter of limitedfrequency range. The loud speaking telephone in which the presentinvention is embodied, is

In accordance with the present invention, Wave filters may beconstructed that possess not only the property of frequencydiscrimination` but also that of wave motiontransformation without lossof energy. Such filters may, therefore, be used advantageously inselective transmission systems. the number of transformers requiredbeing reduced thereby. The elimination of transformers, however, is notthe only advantage of the invention; impedance transformations may bemade at several points within a wave filter without affecting theoverall ratio of transformation, but permitting the magnitudes of theindividual reactances to be changed to such values as may be mosteconomically obtricity are but special cases of the general dynamicallaws of motion. The extension of the wave filter theory, in so far as isnecessary for the proper understanding of the invention, to other modesof motion will be facilitated by noting the analogous properties ofmotion in various systemsset forth in the following table:

Mechanical motion Electric motion Linear 'Angular' Force Torque E. M. F.Displacement.. Ang e. Quantity ofelectrlcity. Velocity Angular velocityCurrent.

Ma Moment annex-tia.. Inducmn, Elastance... Torslonal elastanee 1cgpacity. Flexiblllty Torslonal exib|1ity Capa ty.

Frletlon Friction- Resistance.

The terms mass, elastance, and flexibility define total properties ofstructural elements which are related to the specific quantities,density and elasticity. The reaction forces that a body opposes to an1mpressed force comprise components equal to the product of its mass andthe acceleration of its motion and of its elastance and displacement.These are analogous to the back E. M. F.s in an electrical' circuit dueto the rate of chan e of current in an inductance and to thedlsplacernent of electricity in a capacity. The quantitative relationsbetween the properties of mechanical and electrical systems follow fromthe fact that energy is measured in the same absolute unit, the erg, inboth systems. Motions in the two types of system are comparable if thereactance properties of the elements and the displacements are allmeasured in the absolute or c. g. s. units. In a composite system inwhich energy is translated from the electrical to the mechanical form,or vice Versa, a factor relating to the velocities or the displacementsin the two modes of motion must be known before the motions throughoutthe complete system can be determine In the foregoing table, theanalogous quantities of both linear and angular motion are listed, butin the detailed description of mechanical systems which follows, thenomenclature relating to the linear type of motion will alone be used.The type of motion `actually occurring will be understood from thecontext.

The analogy between .electrical resistance and mechanical friction isnot always complete; a constant electrical resistance is characterizedby its property of dissipating energy at a rate proportional to thesquare of the current, and mechanical friction, to be analogous, musthave the property of dissipating energy at a rate proportional to thesquare of the mechanical velocity. Ordinary mechanical friction does notpossess this property and it is generally necessary to employ some formof fiuid friction to obtain the equivalent of electrical resistance.

In electrical systems, itis easy to obtain structural elementspossessing practically pure inductance or pure capacity by the choice'ofparticular forms and materials in which one property predominates andthe other is. diminished. In like manner may elements possessing simpleproperties with reference to the other systems of motion be obtained.For example, a thin flat air space having its plane placed transverselyto the direction of motion -has compressibilitywith substantially nomass while a very narrow column of air having its Iaxis in line with.the direction of motion possesses mass with substantially no.compressibility. y

The nature of the invention and the manner of its application will beunderstood from the following detailed descriptiontaken in connectionwith thefaccompanying drawings of which; 1^: y

Figures 1, la and 25* are for the purpore o f illustrating the theory ofthe invention.

Figures 3 and 3a show in schematic forni an electric wave filter and amechanical analogue for the purpose of comparison with Figures 4 and 4which represent the same filter modified to effect wave motiontransformations.

Figures 5 and 5 represent respectively a non-transforming wave filterand a wave filter of corresponding properties in which the invention isembodied to simplify the structure.

Figures 6 and 6 illustrate a similar applivcation of the invention.

Figure 7 shows a loud speaking telephone receiver embodying theinvention.

Figures 8 and 9 are additional views of the receiver of Figure 7 toillustrate more clearly certain elements of the system, and

Figures l() and 1l illustrate in schematic form the wave lilter'systemof the receiver shown in Figure 7.

Two important equivalences by means olf which the explanation of theprinciples of the invention is greatly simplified are illus trated inFigure l and l and Figures 2 and 2a respectively.

The four terminal network of Figure. l comprises a shunt impedance ZAwhich is unrestricted as to form and an ideal transformer T. Thetransformer T is assumed to have windings of infinitely greatinductance, perfect coupling and zero resistance. Further,

lll)

liti

the self ilnpedances of the windings, although ,-Figures 1a and 2 cannotbe physically emZ infinitely great, are assumedto bear a finite constantratio as expressed by the equation -Z-= (l) in which Z1 and Z2 denoterespectively the primary'and secondary impedances and 4 is the ratio oftransformation. Such a transformer could neither store nor dissipate anyenergy and would be equally effective at all from left to right or fromright to left. rlhis may be demonstrated by deriving the formulae forthe received currents in the two networks when they are terminated inequal impedances at their right hand ends and subjected to equal E. M.F.s impressed upon the left end terminals. In like manner, may theequivalence of the networks of Figures 2 and 2a be proved. It followsthen that a three element T network in which each element has a finiteimpedance may be substituted for an ideal transformer having a finit-eimpedance connected in parallel with one of its windings and that a Hnetwork of finite impedances may replace an ideal transformer having afinite impedance connected in series with one of its windings. Theimpedance -elements in the networks of Fig'. 1L and Fig. 2a arerespectively related by simple numerical faetors to the impedances ZAand ZB of the prototype networks. These impedances may consi st ofsimple reaetanees or -resistanees ory they may comprise reaetances andresistances in a complicated network in which case the branches of theequivalent networks consist of networks of similar form having theimpedances of corresponding elements constantly related. Further,however, in the network of Fig. 1 the two series branch impedances arenecessarily of opposite sign and in the network of Fig. 2a the two shuntimpedances are also opposite in sign. To make the construction of thesenetworks possible under all circumstances,it would be necessary to haveavailable elements corresponding to both positive and negative mass. orinductance, and to both positive and negative iexibility or capacity.Under 'certain circumstances, negative flexibility may be realized, aswill be seen later, but in general this and negative mass are propertiesthat cannot be imparted to any simple structural element.

Application to electric wave filters. Although the transforming networksof bodied by themselves, yet they can be incorporated into wave filtersand other structures, lthe only requirement being that there should beavailable in the network at the point where the transformation occurs,elements having corresponding positive properties of sufficientmagnitude to absorb the negative properties of the transforming network.For example, the electrical filter structure of Figure 3a may bedesigned, in accordance with the principles and formulae given in thereferences hereinbefore mentioned, to operate between terminalimpedances of equal magnitude. The inductances and capacities sodetermined are denoted by the letter L and C with numerical subscriptsto identify their location in the circuit. These quantities are relatedto the terminating impedance, which 1s shown as a resistance R1, byfactors involving the filter cutoff frequencies; it is not necessary,however, for the understanding of the present invention that thesefactors be known.

If it is desired to adapt the filter to unequal terminating impedances,recourse may be had to the use of one or more efficient transformersinserted at any points in the system.l Let it be assumed that twosuccessive stepdown transformations are desirable, the first .being madeby the insertion of a transformer at the point indicated bythe dottedline A--A and the second by a transformer inserted at BeB. In order thatno internal reflection losses may be introduced the insert-ion of thetransformers requires a modification of the constants of the filterimpedance elements. If the first and second transformation ratios arerespectively denoted by (t, and d), then in accordance with well-knownprineiples of circuit design, all elements to the right of AA must bemodified to have impedances equal to #12 times the impedanees of thenormal design and those to the right of BB must be further modified tohavcvimpedances reduced from the normal values in the total ratio 351295,2. The filter thus modified is found -upon inspection to include aCombination of the type shown in Fig. l, namely the combination ofmodified capacity e120, and the transformer inserted at BB',

v were both assumed to be less than unity, eorresponding to step-downtransformations,

lun

, and also a combination corresponding to Fig. f

the substitution of the II network equivalent to the combination of Lsand the transformer results in'a .negative inductance in parallel withthe combination L1,C1,L2. It is not obvious that this combination canabsorb the negative inductance in parallel but it is made evident by theapplication of a useful equivalence pointed out by Zobel in thereference hereinbefore mentioned. According to Zobel the combinationL'ICIL2 may be replaced by a parallel combination comprising a singleinductance of value (Lft-L2) in parallel with a series resonantcombination of an inductance The effective inductance of Lft-L2 incombination with the negative inductance of the first transformingnetwork will have a positive magnitude so long as the inducta-nce(Lft-L2) is the smaller and consequently may under this condition berealized in a physical structure. lli'he modified capacity C4+1222 willalso combine with the negative capacity of the second transformingnetwork to produce a resultant positive capacity so long as the formercapacity is the smaller. It is a simple matter now to write down theinductance and capacity values of the ele-` ments of Fig. 4 interms ofthe values in Fig. 3 bearing in mind that in the transformationinductance and capacity values must be modified in opposite senses. Thevalues follow:

cieca-a and a capacity The dropping out of this condenser illustratesimpedange of the transforming networ It isevident that formula (3) undercertain onditlons denotes an infinite capacity, the lmpedance of whichis zero.

`Application to mechanicalacaoe filters. The application of theforegoing principles to mechanical Wave filters is illustrated in Figs.3'1 and 4 which represent in a conventional manner mechanical wavefilters for torsional vibrations analogous tothe electrical filters ofFigs. 3 and 4 respectively. In the filter of Fig. 3al the tortionalvibrations are transmitted through a chain of elements rotatably mountedupon a fixed shaft 6. Motion is imparted to the system by torsionalforces impressed upon a driving disc v9. Resistance to motion is presentin the inertia and elastic reactions of the several elementsconstituting the chain, the impedances corresponding respectively to theinductive and the capacitive reactance's of the electrical system. Themasses m1, m2, m3, m4, and m5, furnish the inertia reactions; theelastances are provided by springs having iexibility to torsional forcesonly and are denoted by Sl, S2, S3, S4, and S5. To eliminate the effectof gravity as a controlling force the masses are arranged in pairsbalanced about the'centre line of the sha-ft; for symmetry theelastances are also arranged in balanced pairs. The pair of masses m1corresponds to the inductance L1 of Fig. 3, the elastances S1 correspondto the reciprocal of the capacity C1, and so on throughout the tWosystems. The fixed shaft 6 corresponds to the common connection betweenthe terminals 2 and 4 of Fig. 3. The successive series branches fromleft to right between the terminals 1 and 3 of the electrical filterhave their counterparts in the rotatable sleeves 5, 8 and 7 and theelements attached thereto. The shunt impedances are represented in themechanical structure by systems vof masses Vand elastances attached tolight rigid spindles adapted to rotate about the main shaft in a planeperpendicular thereto and to be capable of motions distinct from thoseof the series elements. These impedances comprise the elements m1 m2 andS1 and also the elements m4 and S3. The connections between the seriesand the shunt arms are made through bevel gear wheels 10 and pinions 11the latter being arranged to rotate freely upon shunt system spindles.The ,effect of the resistance R1 in which the electrical filter isterminated is obtained in the mechanical system by means of a conductivedisc 13 attached to sleeve 7 and rotating between the poles of permanentmagnets 14.. The interaction between the flux of the magnets and theinduced currents in the disc produces a drag which is proportional tothe velocity of the motion of the disc and is therefore a correctanalogy of constant electrical resistance. The springs S2 and Si Whlchcontribute part of the series branch impedan'ces are shown with theirouter ends connected to external abutments 12 which may be regardedeither as fixedpoin'ts or as masses of infinitely great inertia. rIthe shunt combination L40., of Fig. 3 appears 1n Flg. 3 as two separate shuntsystems in one of which the masses m4 is driven b a bevel gear systemand in t-he other of whic i a light spindle, restrained from motionabout the shaft by the coiled springs S3, is similarly driven.

The similarity of the transmission characteristics of the two systemsmay be demonstrated by examining their actions under corresponding typesof impressed force. A torque applied to the driving disc 9corresponds toan E. M. F. applied to terminals 1 and 2. If theE. M. F. applied to theelectrical filter is steady and unidirectionaL'the resultant currentwill be confined to inductances L1 and L2 and will be limited only bythe slnall resistances of these elements. The condenser C2 will blockthe current How inthe other branches of the circuit but there will be anelectrical displacement in each of the condensers dependent on theirrelative capacities. Similarly a steady torque appliedfto the mechanicalfilter will result in a continuous motion of the masses m1 and m2 butthe remaining parts will beheld fixed in slightly displaced positions bythe restraints of the various springs.

An EM. F. of the frequency at which the combination L .,C5 is resonantwill be strongly attenuated. The total current in the second seriesbranch will bepractically zero although a large circulating current willflow around the closed resonant circuit. In the mechanical system avibrating torque of the frequency at which the combination MSS5 isresonant will produce practically zero motion of the sleeve 7. Thecombination m5S5 isequivalent to 'a series anti-resonant electricalcircuit at resonance the mass and the spring oscillate violentlythemselves but impede strongly any motion of the point of support 7 Thesystem m, is of similar type and therefore at some frequency causes theshunt arm to have an infinitely great impedance, a like effect beingproduced in the electrical system at the resonance of L,C,. Atfrequentcies much above resonance the lnass m, tends to remainstationary and the combination ex- I hibits the properties of a springanchored at its outer end. The elastance of the combination at somehigher frequency resonates with the mass m2 causing the latter tooscillate strongly about the shaft 6. W'hcn the impressed torqueproduces resonance of m, and S1 the motion of the mass m2 is practicallyreduced to zero with the result that the whole motion of the drivingdisc is passed on through the gear system to the sleeve 8. Whensections.

thesecond type of resonance occurs the mass m2 1n resonance follows thesynchronous impressed force` so readily that the whole m0- tion impartedto the driving disc is absorbed by the shunt system. The motions ot' thelother parts of the system are similarly related to the currents incorresponding electrical eleed elements constitute the series branchesof the system corresponding tothe successive series sections of theelectrical line fronrleft to right between theterminals 1 and 3 of Fig.4: Corresponding elements are indicated bv hke subscripts in thesame'manner as in Figs. 3 and 3a. The system'm6 is a series-resonant shuntcombination, the characteristi of which are obvious in view of theforegoing explanation. The spring S9 coupling series elements 17 and 18is an alternative and simpler form of shunt elastance, the relationshipof which to the shunt elastance S3- of Fig. 3"L is also readily Seen.The reduced terminating impedance corresponding to R2 is most readilyobtained by reducing the thickness of the eddy current disc 13', theinduction drag being correspondingly reduced-thereby.

` It should be noted in passing that the bevel gear connections of theshunt elements reduce the angular velocities` of these elements in therat-io of two to one and reverses the direction of motion betweensuccessive series These effects are the same as would be produced in theelectrical system by the introduction of a pair of equal ideal two toone ratio transformers at each shunt branch.'

They are immaterial with regard to the overall properties of thefilters, but in applying filter formulae to the computation of the shuntmasses and elastances due allowance for the velocity transformation mustbe made.

The velocity transforming property of the mechanical filter of Fig. 4 isobtained not by the useof reduction gears which are closely analogous toidea-l transformers but by the modification of the elastic and inertiaconstants of the system in accordance with the principles of theinvention. The relationships previously listed between the coefficientsof the elements of Figs. 3 and 4, hold also between those of Figs. 3 and4** when masses are substituted for inductances and fiexibilities or thereciprocals of the elastances, are substituted for capacities.

It should be observed that a characteristic feature of the shuntelements is their capability to absorbsome of the velocity of a serieselement thereby reducing the velocity in a subsequent series element. Inthe mechanical systems described above the series and llt) shuntimpedances occupy relative positions closely similar to those of thecorresponding electrical impedances but in other mechanical systems thearrangement may have but little correspondence to the conventionalelectrical arrangement. In such cases, the above-noted feature of shuntimpcdances is helpful in distinguishing them from series impedances.

Systems hauling fu/mgue values of transfo/rmatz'on ratio.

The systems of Figs. 5, 5, 6 and 6 illustrate the application of certainlimiting values of thetransformation ratio for the pur ose of reducingthe number of impedance e ements required in a given filter. Forsimplicity the electrical conventions are used in these figures but inview of the foregoing description, it is evident that they may representconventionally wave filters for motion of any type.

The filter of Fig. 5 comprises two complet-e mid series terminatedsections of a. wellknown type and is ofsymmertical form suitable foroperation between equal terminating impedances. The full seriesinductance is relatedl to the full shunt inductance L by a constantfactor a the nature of which will v be described later. The filter maybe modified for efficient operation between unequal impedances byeffecting transformations at the sections DD and FF in accordance withthe methods already described in connection with Fig. 3. In thisinstance, both transforma-tions are effected by substitutingfor y theshunt inductances T networks of th-e type shown in Fig. la. Denoting thetransformation ratios at D and F respectively by qbD and F, expressionsfor the constants of the elements in the modified filter are readilyobtained. The central series branch will contain a capacitycorresponding to the original capacity C but modified in accordance withthe transformation ratio ein, It will also contain an inductance whichis equal to the sum of the transformed inductance corresponding to alland the components lcontributed by the inserted T networks. The value ofLQ-of this resultant inductance is given by the equation Le= f 1 2aL-D(1 D)L+D2f1 F)L (4) and is zero under the conditions expressed by thefurther equation By a proper choice of the transformation ratios a newstructure, as shown in Fig. 5", is obtained which has one less elementthan the network of Fig. 5 but which possesses the same transmissioncharacteristics as the latter network together with an ideal transformerhaving a ratio D qbF.

The following particular cases are of importanoe.

transformation.

Fasain which F=1+D. The double sectlon 1s adapted for operation betweenequal impedances, the transformation ratio being given by the equationSecond, in which (pF is unity. Only one transformation is made the ratiobeing l mi (7) Third, in which F=D. This represents the case of aAuniformly tapered line of similar sections. For this case The two valuesindicated by the plus and minus signs are reciprocally equal, onecorresponds to a continued step up transformation from left to right andthe other to a continued step-down transformation. A difficulty arisesin the termination of a structure of this type as the final step downtransformation leaves in the end series arm a negative inductance whichis large enough to balance not only the natural full series inductanceof the arm but also the component that' would be added by a furtherstage of transformation.` A mid series termination would thereforerequire the use of an element having negative inductance andconsequently could not be embodied in any physical structure'. Ingeneral, however, after several stages of step-down transformation theactual magnitudes of the series inductances would be relatively verysmall and the elements'could be omitted without noticeable effect uponthe transmission characteristic. In certain cases an additional filtersection of a different type may be added in which the series inductanceis large enough to balance the negative inductance due to the last For adiscussion of the principles governing the connection of filter sectionsof different types reference is made to the aforementioned article byZobel.

Another example of the application of the invention to the reduction ofthe number of elements in a filter network is illustrated by Figs. 6 and6, the former representing a two section mid-shunt terminated filter ofsymmetrical structure, and the latter representing the structureresulting from special transformation effected at the points GG and HH.In this instance, a shunt inductancc has been eliminated.

The condition 'for the elimination of the shunt element is expressed bythe equation b=12E+GE H in which b is the ratio of the full series inlonductance of Fig. 5 to thel full shunt inductance, and ifm qSH arerespectively the transformation ratios at pointsG and H. In the twocases illustrated the factors a and b are each equal to in which f1 andf2 are respectively the lower and upper cutoff frequencies of thefilters. rlhis follows from a comparison ofthe formules for theconstants of these filters given in U. S. patent to Campbell No.1,227,113, May 27, 1917. The more general design formulae in the4 Zobelreference hereinbefore mentioned show that any series element is relatedto any shunt element of the same kind by a constant factor which dependsonly upon the ratios of the cutoff frequencies and the frequencies ofinfinite attenuation.

rlhe types of filter section in the joining of which an impedanceelement may be eliminated are principally those in which either theseries or the shunt arm includes only a single element. It is I notnecessary, however, that the sections joined be of the same type as wasshown in connection with the description of Fig; 4f When the filtersections are of unli e types a ratio corresponding to a or b may befound from the co4 eflicients of the -completed filter as designed forsymmetrical termination and the proper ratio computed therefrom.

Application afin/ventina to loud speaking f telephone.

. a perfect reproduction of the electric current rlhe second is toeffect, thel undulations. translation ci all the electric energy intosound wave energy. The production of sound waves is most efficientlyaccomplished by the use of a mechanical device to produce displacementsot the air and in consequence it is customary to convert the electricwaves into an intermediate mechanical motion.

The achievement of high eiciency in the two translations requires thatthe impedance at one end of the mechanical system must equal that of theelectrical system. and the im ed- (ill ance at the other end must equalthat o the acoustic system. In general, some kind of transforminglinkage must be used in the mechanical system" but with practical mateirials and structure forms it is extremely difficult, if not im ossible,to construct a mechansxn of this kind, the elements of which do p artsare proportioned to cooperate in functioning as a band filter having atransmission band Wide enough to include all frequencies needed for thehighest quality reproduction and also to eii'ect whatever wavetransformation is needed for efficient transfer of energy.

'The mechanical moving system comprises two groups of elements, one ofwhich transmits torsional vibrations and the other longitudinalvibrations. The first group includes a light but relatively stiff shaft20 to one end of which is rigidly attached a balanced magnetic armature19 having the form of a double ended wedge, and to the other end ofwhich is attached a rectangular cross bar 22. The Yshaft 20 is supportedon a. wedge pivot block 23, the sharp edge of which engages. with alongitudinal V groove lcut to the centre line of the shaft. The angle ofthe groove is slightly greater than the angle of the pivot block so thata limited angular motion is possible. The block is supported upon thebase 24 which forms part of the rigid framework of the apparatus. Tohold the shaft firmly in place without interfering with its rotationalmotion the centre portion of the V block is cut away and a light stiffwire 25 passing through two holes in the end portions of the blockengages with an eye in the threaded pin 26 attached to the shaft. The

motion of the armature and shaft is resisted by a pair of leafcompression springs 27 which are attached at one end to the cross bar'22 and at their other ends to the base 24.

The second group of parts, in which the motion is longitudinal, includesthe receiver diaphragm 30 and the spider element 3l the toes of whichare riveted to the diaphragm.

The purpose of the spider element is to im- 4 press the driving forceupon the diaphragm in such a manner that the latter moves nearlyuniformly over its whole surface, thereby acting like a rigid pistonupon the air in the chamber 29. Since this elementshould be made aslight as possible it is difficult to avoid iiexibility in itsconstruction and it is more practical to proportion the elastance tocooperate with the elastances of the other elements to produce a desiredtransmission characteristic. The air in the chamber 29 in front of thediaphragm also constitutes an element of this group, the form of thechamber being such that the elastance of the air body is itspredominating property. The diaphragm is constructed to act as nearly aspossible like an air-tight frictionless piston of negligible mass. Tothis end it is made of thin aluminum foil and is provided with circularcorru gations to give it rigidity. The edge of the diaphragm is clampedto the walls of the air chamber by a clamping ring 32 thus ensure ingair-tightness but at the same timeintroducin a slight resistance to,motion due to the e astance of the diaphragm. The two groups areconnected by the angled rod 28 one end of which is riveted to t e centreof the spider 31, the other end being rigldly connected to the end ofthe cross bar 22. .Besides acting as a means for converting rotationalto longitudinal motion, the bent section of this rod provides an elasticconnection between the two groups of elements.

The electrical and the mechanical systems are coupledelectromagnetically. The armature 19 is placed between two U shaped polepieces 21 of a permanent magnet 33 and 1s normall held y the springs 27in a symmetries position relatively to all four pole faces. Encirclingthe armature but notA mounted thereon or in any way attached are theenergizing coils 34 through which flow the s eech currents. An electricsource 35 is in icated in the electric circuit the internal impedance ofwhich is represented by the resistance 36. The connection between thesource 35 and the coils 34 includes electrical filter elements 37 and38.

The terminatingl load at the acoustic end of the system is an amplifyinghorn 39 the throat alone of which is illustrated. The type of horn thatshould preferably be used is the exponential type described in thecopending application of H. C. Harrison, Serial No. 628,168 filed March28, 1923 and also by Hanna and Slepian, The :function and design ofhorns for'loud speakers, Transactions of American Institute ofElectrical Enineers, March, 1924. The advantage of this orn is that itoffers a constant and purely dissipative load at all but very lowfrequencies to pressure forces impressed upon it, that is, it isanalogous to a constant resistance load in an electrical circuit.

To secure an ecient magnetic structure it is nry that the air gapsbetween the armature i9 and the pois faces be small and in consequencethe motion of the armature must also be conned to minute displacements.That part oi' the moving system must therefore be sti or in other wordshave a high impedance. The input impedance of a horn is generallyconsiderably lower than that of the armature and the moving system inconsequence will generally be arran 'ed for stepping down in impedance.In t ustrated the over-all impedance ratio is the resultant of severalintermediate transformations each having for its object the moreeffective couplin of successive elements to enable them to notionproperly as elements of a uniform ilte y lllethodo/ design. The methodof ap lying the present invention in the design o the system will bemore easily understood by referring to Figs. 10

e system il-wmenus and 1-1 which re resent the equivalent electricalcircuits. Fig. 10 the mass of each mechanical'ele'm'nt is Indicated byan inductance symbol and the elastances by capacity symbols. Theeffective mass of each element s is designated'by the letter m with anumerical subscript corres ending to the reference number used toesignate the element in Figures 7, 8, and 9. The elastances aredesignnted in a similar manner. The acoustical portion of the system isrepresented bythe shunt elastance S2, and the horn resistance R59 thetwo being coupled through a transformer 40 which represents thetransformin action of the connection between the enlarged air chamber 29and the narrow aperture of the I' :i

horn. P The mass Dand elastance coeicients referring to the elements 1nwhich the motion is linear are the linear coeilicients modified to bringthem into uniformity with the coeilicientel of the elements havingangular motion.

'The linear masses are multiplied by the square of the radius from .thecentre ofthe shaft 20 to the centre line of the linear motion to Thelinear elastances are divided by the same factor. The lineardisplacements are equal to the angular displacements multiplied by theradius and the linear forces are equal to the torsional moments .dividedby the radius. The element 41 re resents the cou ling impedance. betweent e electrical an the mechanical systems. The theory of this type ofcouipling is given by R. L. Wegel,Theory of Tele one Receivers, Journalof A. IgE. E. Vol. LNo. 10, Oct., 1921. The coupling impedance isdefined as the ratio of force in the mechanical system to the currentinthe electrical system, and conversely as the ratio of the back E. M.F. in theelectrical system to the velocity in the mechanical system. Thetwo ratios are equalfand have the same value at all frequencies but areof opposite sign.

The elastance S19 represents the control of the armature duel to theattraction of the .permanent magnet poles. When the armature is in acentral position the attractions of all four pole faces are balancedbutif it is slightl dlsplaced the attractive forces are increase in thesmaller air gaps and decreased in the larger, the result being anunbalanced force tending to increase the displacement. In a magneticsystem of the ty c described the torque due to the field issurbstantially pro ortional to the angular displacement of t e armature.The ratio ofthe torque to the displacement is therefore of the nature ofa negative elastanoe. The value of S1 may be shown to be equal to normalair gap length, the distance from the centre of the armature to thecentre of give the equivalent angular masses.

liti.'

llo

lll

the pole faces, and B is the fiux density of the permanent magnet fiu'xin the a1r gap.

Fig. 11; represents the uniform bandpass filter to which Fig. ispotentially equivalent; that is to sayif the 'elements of Fig. 10 areproperly proportioned the system may be made to possess all. thecharacteristics of the band filter of Fig. 11. It will be noted thatFig. 11 includes two transformers-l2 and 43; these are idealtransformers which with their associated shunt elastances are replacedin Fig. 10 by Tne-tworks of elastances proportioned in accordance withthe values shown in Fig. 1a. The first transformation is introduced topermit the real negative elastance of the field S10 to be incorporatedin the filter. In the design of electrical transforming filters it waspointed out that the negative branches of transforming networks couldnot be embodied separately in any physical structure and as a resultcertain limitations are placed u on the possible transformation ratios.In t is instance the negative elastance has a real existance and may beused as an actual filter element.

When the. transforming T network of Fig. 10 is replaced in Fig. 11 bythe combination of an ideal transformer and a shunt elastance there mustnecessaril be left in each adjacent series arm a residual positiveelastance to maintain the proper band pass filter characteristics. Thesection of Fig. 11 between the lines J J and KK includes the couplingimpedance and two series impedances. On the mechanical side the seriesimpedance is made up of a mass denoted by 1/2mq, and an elastancedenoted by j/gftp These are parts respectively of the armature mass m1and the residual positive elastance of the series branch of thefiltertheir fractional values being so far undefined. The electricalimpedance includes an inductance 1L/2Lp and a capacity 2C., which,similarly, are fractions, at present undefined, of the elements L3* andC38. The magnitude of the mechanical impedance is denoted by pM thefactors of which may also remain undefined at present. The impedances ofthe series arms of the section may be denoted respectively'by thegeneralized impedance symbols 1/2Zq and 1/Z.

It follows by a short analysis from the equations given b Wegel intheaforementioned reference t at the proper impedances in which the sectionshould be terminated to avoid reflect-ion loss are given by theequations Ze being impedance on the electrical 'side and Zm theimpedance on the mechanical side.

If Zp and Z.l are linearly related the factor il p may berdefined as theratio lform as the mid series iterative impedance of the so-calledconstant la type of band ass wave filter described by Campbell an byZobel, that is, a filter in which the product of the series and shuntimpedances is constant at all frequencies. It follows therefore that thesection may be connected at J J and KIQl to mid series, terminatedconstant c filters having the same type of series impedances as Zp orZq. In the Zobel reference it is pointed out that certain other types offilters which are not of the constant lo type are also capable of beingconnected to constant lo sections, a principal condition being that theseries impedances should be of the same type when the connection is tobe made between mid series terminated sections. In the systemillustrated the type of filter sectionused is suitable for connection tothe constant c coupling section. The factor p2 evidently represents atransformation ratio but since it relates me- ',chanical to electricalimpedance it is not a pure numeric. The factor M is the force factor fora symmetrical system in which the transformation is unity.

That the coupling section has transmission characteristics also similarto those of a band filter may be seen by considering its physicalproperties when it is terminated in the impedance ZB and Zm. If theseries impedance 1/Zp contain only pure reactances, Ze and Zm may atdifferent frequencies be either pure reactance or pure resist-ance butcannot be complex. No energy can enter or flow through the system whenZ., and Zm are reactive, consequentlv the pass band frequencies must be.those for which Ze and Zm are resistive. The limiting frequencies of thetransmission band are found to be:

f were s lm 1 21r1 ma,2 1n.l may lVPp4 Sq Mp f2 2{ mq, JfmemI2 'Inhehalf series impedances of the filter sections connected to the couplingsection comprise on the electrical side the capacity QCP and theinductance l/ZLp, and on the mechanical side the mass V2M',l and theelastance lgSq. These quantities are related to the correspondingcoefiicients ofthe coupling section seriesbranches by factors thatinvolve ployed the following relationships are found:

2 2 seisLZ t 2 (3 j:

in which Sr is the residual positive elastance of the mechanical seriesbranch.

The force factor pM for the magnetic strunture illustrated is given bythe equation:

The factor B, A and Z having the same meaning as in formula 11. Thefactor al denotes the fraction of the total ux of the energizing coilsthat is effective in the polar air gaps. From equatlons 14,*bear1ng 1nmind that p defines the ratio of"m0 to L0, and expression may be foundfor the band Width in terms of the negative elastance and the arma turemass, namely:

The band Width is thus determined completely by the dimensions of themagnetic structure, and the manner of proportioning the parts to securea large band Width is indicated. The actual location of the band remainsto be determined. This may be done by considering the relationship thatmust exist between the elastances S19 and S20 to maintain the filtertransmission characteristic. Applying the formulae relating to theequivalence of Figures 1 and la to the coeicients of Figures 10 and 11it is found that s.s.= 1 d, Si. 18

9ST being the ratio of transformation of transformer 42.A From theformulae for the coeiiicients of .the filter sections it is also foundthat:

`Further it is found from Athe filter formulae that Sao 'mu'r zeef-ff)21) and finally from equations 2O and 21 quencies, the lower limit couldtheoretically be placed at zero but this is obviously impracticable asit would require that the Whole mechanical system move continuouslyunder the influence of a direct current input. In practice a lowerfrequency limit of about 100 c cles per second is commonly used. Theclioice of the band limits determines the elastance S20 of the shaft 20;the transformation ratio qbT is thereafter determined by equation 21.The coefficients of the remaining mechanical elements are related to thearmature mass m0 and the elastance S20 in terms of the transformationratio dan, the ratio 4m of transformer 43, and the factor connecting theseries and shunt elastance of the'lter. As the series elastance S31associated in Fig; 11 with the mass m31 of the spider element is zero inthe actual system the transformation ratio 4 U must have a speciallimiting value such as obtains in Figs. 5a and 6a. The Value of 96u isfound to be v The expression for the masses and elastances are thefollowing gizing coil 34 by the equations Ihe primary factors in thedesign of the system have been shown to be the angular mass m0 of thearmature, the field elasticity S10 and the leakage factor d of theenergizing coils. The angular mass m0 of the armature is most readilydetermined from its geometrical dimensions butgeometrical formulae forthe other two factors become very com lex if high accuracy is re hired.These actors may be determined with accuracy from im- Leemans equivalentto opening the circuit ofFig. 10 at the connection of m22 to S20. Underthis condition the impedance to an alternating E. M.

F. im ressed directl upon the terminals of the coil 34 maybe s own to begiven by the` equation ,PM2 ZP *Rr +.727VLP" S20 +Sm.. (26) 1rfmq --27 fin which RP and LP are. respectively the efectiveresistance and theinductance of the coils 34 and the armature atrest in its normalposition.- The impedance ZP is the impedance of thesystem measured atvthe coil terminals, or the' apparent-impedance of the coil when thearmature is in motion. If the impedance -is measured at a large numberof frequencies covering a wide range, a resonance value will be foundwhich corresponds to the resonance of the armaturemass m2 and theresultant elastance, S10 S20. lf this resonance frequency is denoted byf. the resultant elastance is expressed by I Similar measurements madewith the permanent magnet removedso 'that the field elastance S19 isnegligibly small determine the fre- 4 quency at which the mass-of thearmature quencies gives both elastance S10 and S20. It

Will-be noted that the requencyff, according to equation (22) is the midrequency of transmission band, in practice it is generally between 2000c. p. s. and 3000 c. p. s.

The factorfd ma be found bycomparing at some relatively onf-frequency,preferably between 400 c. p. s. and 800 c. p. s., the apparentinductance of the system while the armature is in motion with theinductance while the armature is at rest in its central position.' Todetermine the latter inductance the armature must be held rigidly in itsnormal position of rest. It the value of the force factor pM given byequation (16) is substituted in equation (26) an expression fort-hefactor d can be found, namely ture and f is the frequency at which Lp ismeasured.

An advantageous feature of the structure described is that the controlofthe system. by means ofthe springs 27, being effected in a differentsection of the filter, does not add to themass ofthe armature andtherefore does not diminish the possible band width.

This controlisnecessary yto stabilize the system in the`presenceof 'thenegative elastance of the tield and `if applied directly to the armaturean undersirable mass is added thereto-by the springs themselves and themeans of attachment so that the transmission rangeis noticeably reduced.Further the ste -up transformation between the armature an the pressedforce to the velocity resulting therel rom. The force may be electricalor mechanical and if mechanical may be in the nature ofl a simple linearforce or a torsional moment or again an excess of pressure over thenormal pressure of a gas. The velocity or intensity of motion in eachcase'must be of a corresponding type, actually it is the quantity theproduct of which with the force gives the time rate of change of energy.The terms reactance and resistance when used in the claims define theimaginary and the real components of impedance and by analogy have thesame breadth of application as the term im-. pedance. v

To define the properties of an element whereby it offers a reactiveimpedance to an impressed force the terms inertia and elastance wiil beused in relation to both mechanical and electrical systems.

The general sense of series and shunt connection has -been made clear bythe detailed description of the properties ofthe analogous Y Z3=Za inwhich Z and Zil are respectively the series and the shunt impedances ofa symmetrical T section adapted to cooperate directly with one of saidfilter portions in maintaining the broad band frequency selectivity.

2. A broad band wave filter section comprising in the form of anunsynimetrical T network series impedances denoted by Z1 and Z3 QSZM inwhich is a constant numerical quantity different fromunity, whereby theunsymetrical section is adapted to transform the wave motion in theratio 4 while at the Sametime maintaining the transmission band limitsof the prototype section.

3. In combination in a broad band wave filter a three branch network ofreactive impedances the magnitudes of which are related by constantfactors at all frequcncles, two of said impedances being of oppositesign, and the values of said impedances being proportioned with respectto the other impedance clement-s of the filter to produce atransformation of the amplitude of waves traversing the filter while atthe same time maintaining the wave selective characteristics.

4. In combination in a broad band wave filter a network comprising agroup of three elastances, two 'of which enter into series branches ofthe filter, and the third being ineluded therebetween as a couplingelement,

the elastances inthe series branches being opposite in sign to eachother, and the mag-` nitudes of said elastances being proportioned withrespect to the remaining elements of the filter to roduce atransformation of the motion o waves traversing the filter while at thesame time maintaining the wave selective characteristics.

5. In a wave filter, an unsynimetrical filter section adapted totransform the intensity of wave motion and including, for the purpose ofsaid transformation, a network of three reactive impedances of like typeone of which has a negative value with respect 'to the other two, asecond filter section connected to said unsymmetrical section, apositive impedance in said second section of like type to said negativeimpedance, said positive impedance and said negative impedance beingcombined to produce a zero resultant impedance.

6. In an electromagnetic device for translatinol electric wave energy.into the energy of mechanical motion, al magnetic armature, a constantpolarized field therefor, whereby said armature is subject to thecontrol of negative elastance, a moving system comprising a chain ofconnected inertia elements and elastance elements constituting a broadband wave filter, an elastic couplin between said armature and saidsystem an a series elastance in said system, said series elastance beingproportioned conjointly with said neglative elastance and said elasticcoupling to a polarizing magnetic field therefor, whereby said armatureis controlled by a negative elastance, an inertia element coupled tosaid armature by an elastic coupling element and restrained from freemotion by a second elastic element, said negative elastance and theelastances of said coupling element and said second element being soproportioned in conjunction with the masses ofb said armature and saidinertia element to constitute a broad band wave filter section adaptedto translform the amplitude of mechanical vibrations impressed upon saidarmature.

8. In an electromechanical broad band wave filter an unsymmetricalsection comprising a T network of reactive impedances and having anelastance included in each branch, the elastance in one series branchbeing of negative sign, and the three elastances being proportloned toeffect atransformation of the wave motion While at the same timemaintaining the wave transmission `characteristics of the filter.

9. A composite electrical and mechanical wave transmission systemcomprising an electrical network, a connected chain of mechanical'elements and an electromagnetic wave translating device, said networkand said chain of elements and said translating device includingreactive impedance elements disposed in series and shunt relation andproportioned to constitute a band pass wave filter having band frequencylimits both different from zero, and said mechanical system includingunsymmetrical sections adapted by the sense and degree of theirdissyminetry to transform the amplitude of the wave motion in apredetermined ratio, while at the same time maintaining the wavetransmission l iso band pass filter adapted to transmit vibrationsaccording to its typical mode of motion, and said coupling elementfunctioning to translate the motion from the one mode to the other'.

11. An impedance transforming wave filter adapted to transmitselectively waves in a desired broad band of frequencies, comprising twoportions having unequal characteristic impedances, and a couplingsection included between said portions, said coupling section comprisingan unsymmetrical system tem of connected impedances having precom` putedvalues dependent upon the limiting frequencies of the desired broadbandand upon the unequal characteristic impedanees of the connectedfilter portions whereby the iilter will transmit waves without reectionat its internal junction points, andfwill transform the amplitudes ofthe waves in accordance with ratioof the impedancesof the twoportions.

l2. An unsymmetrical wave filter section comprising a connected systemof series and shunt impedances, said lmpedances having precomputedvalues dependent upon the upper and lower limiting frequencies of arange of frequencies it is desired to transmit, and

.dependent also upon two -preassigned impedance values which are in aconstant ratio different from-unity, whereby the filter section isadapted to be connected between unequal impedances of the preassignedvalues, and when so connected will transmit, with negligible attenuationand without reection waves of frequencies within the desiredspect to theother impedances of the wave filter to co-operate in maintaining thebroadV band transmission characteristic.

14. An impedance transforming wave fil-` ter adapted to transmitselectively waves in a desired broadband of frequencies comprising twoportions having unequal characteris-- tic impedances which are in aconstant ratio, anda coupling system included between said saidportions, said system comprising a group of three similar impedances,the values of which are precomputed with respect to each other inaccordance with the said ratio of the characteristic impedances, and inaccordance with the limiting'frequencies of the desired band, wherebythe coupling system is equivalent to the combination of an impedanceelement of one portion of the lter with an ideal transformer having atransformation ratio equal to the ratio of the charateristic mpedancesof the two portions.

In witness whereof, I hereunto subscribe my name this 21st day ofNovember, A. D.,

EDWARD L. NORTON.

